Adding Mixed Numbers
Find the least common denominator. Adjust the numerator by the same factor as the denominator. Add whole numbers and numerators, but not denominators. Simplify improper fractions.
Subtracting Mixed Numbers
Adjust fractions the same way as for adding. If needed, borrow to avoid a negative fraction with a positive integer. Subtract and simplify as needed.
Multiply Mixed Numbers
Change mixed numbers to improper fractions. Cancel common factors in the numerator and denominator. Multiply straight across. Change improper fractions to mixed numbers.
Divide Mixed Numbers
Change mixed numbers to improper fractions. Rewrite problem as multiplication and changing the divisor (the 2nd fraction) to its reciprocal. (To divide by a fraction, multiply by its reciprocal.) Cancel common factors in the numerator and denominator. Multiply straight across. Change improper fractions to mixed numbers.
Order of Operations with ( ), [ ], Exponents
Start with the inner most grouping symbols. Then do exponents, multiply and divide left to right, add and subtract left to right. Follow this pattern from the inside out. A number next to a grouping symbol means to multiply.
GCF of Monomials
List the prime factors of the coefficients. List the variables, making as many copies as the exponents says. Group any factor common to all the given monomials. GCF = one factor for each group. Multiply the common factors. LCM of Monomials
List the prime factors of the coefficients. Match up any factors that are common to any two monomials. LCM = one factor for each group AND one factor for any others left over in the monomial lists. Multiply these factors together.
All 1 Step equations: The Pattern
Original Problem
Inverse Operation
Identity Step
Answer 1 Step Equations: Add
Find the variable and the constant on the same side of the equal sign as the variable. Subtract that constant from both sides of the equation. Show that x + 0 = new total, then x = answer. New total and answer are the same.
1 Step Equations: Subtract
Find the variable and the constant on the same side of the equal sign as the variable. Add that constant to both sides of the equation. Show that x + 0 = new total, then x = answer. New total and answer are the same.
1 Step Equations: Multiply
Divide both sides of the equation by the coefficient. Cancel common factors in numertors and denominators, especially the coefficient and the divisor. Show that 1 times the variable = new number, then variable = answer. New number and answer are the same.
1 Step Equations: Divide
Multiply both sides of the equation by the number that the variable is being divided by. On the variable side of the equation, show the multiplying number as a fraction to keep numerators and denominators straight. Cancel common factors in numertors and denominators, especially the divisor and the multiplier. Show that 1 times the variable = new number, then variable = answer. New number and answer are the same.
Find the least common denominator. Adjust the numerator by the same factor as the denominator. Add whole numbers and numerators, but not denominators. Simplify improper fractions.
Subtracting Mixed Numbers
Adjust fractions the same way as for adding. If needed, borrow to avoid a negative fraction with a positive integer. Subtract and simplify as needed.
Multiply Mixed Numbers
Change mixed numbers to improper fractions. Cancel common factors in the numerator and denominator. Multiply straight across. Change improper fractions to mixed numbers.
Divide Mixed Numbers
Change mixed numbers to improper fractions. Rewrite problem as multiplication and changing the divisor (the 2nd fraction) to its reciprocal. (To divide by a fraction, multiply by its reciprocal.) Cancel common factors in the numerator and denominator. Multiply straight across. Change improper fractions to mixed numbers.
Order of Operations with ( ), [ ], Exponents
Start with the inner most grouping symbols. Then do exponents, multiply and divide left to right, add and subtract left to right. Follow this pattern from the inside out. A number next to a grouping symbol means to multiply.
GCF of Monomials
List the prime factors of the coefficients. List the variables, making as many copies as the exponents says. Group any factor common to all the given monomials. GCF = one factor for each group. Multiply the common factors.
LCM of Monomials
List the prime factors of the coefficients. Match up any factors that are common to any two monomials. LCM = one factor for each group AND one factor for any others left over in the monomial lists. Multiply these factors together.
All 1 Step equations: The Pattern
Original Problem
Inverse Operation
Identity Step
Answer
1 Step Equations: Add
Find the variable and the constant on the same side of the equal sign as the variable. Subtract that constant from both sides of the equation. Show that x + 0 = new total, then x = answer. New total and answer are the same.
1 Step Equations: Subtract
Find the variable and the constant on the same side of the equal sign as the variable. Add that constant to both sides of the equation. Show that x + 0 = new total, then x = answer. New total and answer are the same.
1 Step Equations: Multiply
Divide both sides of the equation by the coefficient. Cancel common factors in numertors and denominators, especially the coefficient and the divisor. Show that 1 times the variable = new number, then variable = answer. New number and answer are the same.
1 Step Equations: Divide
Multiply both sides of the equation by the number that the variable is being divided by. On the variable side of the equation, show the multiplying number as a fraction to keep numerators and denominators straight. Cancel common factors in numertors and denominators, especially the divisor and the multiplier. Show that 1 times the variable = new number, then variable = answer. New number and answer are the same.